In order to ensure that each estimated ES does not cross the corresponding estimated quantile,
we model ES in (REF ) as the product of the quantile and a constant factor (see, e.g., [1]} and [2]}) as follows:
\(ES_{tj} = (1+e^{\gamma _{0j}}){\cal Q}_{Y_{tj}}(\tau _j), \quad \quad t=1,2,...,T, \quad j=1,2,...,p,\) 
